$f(x) = -x^{2}-3$ What is the range of $f(x)$ ?
Consider the range of $-x^{2}$ The range of $x^2$ is $\{\, y \mid y \ge 0 \,\}$ Multiplying by $-1$ flips the range to $\{\, y \mid y \le 0 \,\}$ To get $-x^{2}-3$, we subtract $3$. So the range becomes: $\{\, y \mid y ≤ -3 \,\}$.